In general, guys wear black boots and women wear white boots. Female show skaters and synchro skaters will often wear tan, flesh-colored boots, which don't stand out as much as the bright white. Coaches who've been in the rink too long and don't compete any more will often go for more colorful boots, flag designs, etc.

Types of Figure Skates

In theory there are three main types of figure skates: freestyle, dance, and figures. In practice most of what you'll see at the rink doesn't fall into any of those categories though, so I'll add two more--rental skates and entry-level skates. There are special synchro skates too, but I'm not sure what makes them different (I'd guess they're like dance boots since synchronized skating doesn't have many jumps).

Freestyle Skates

Freestyle skates are used in freestyle and pairs and designed for doing jumps and spins. Most of the attention in the construction of the boot goes to providing enough anklesupport for the take-offs and landings of jumps. Larger skaters and those doing harder jumps will have more layers of reinforcement in their boots. They take a long time to break in.
Freestyle blades have the longest blade (for speed) and largest toe pick (for taking off and landing jumps).

Dance Skates

Dances skates are used solely for ice dancing. The boots are softer, have a lower ankle, and are generally designed for more knee bend with less effort. The blades have shorter heels (roughly an inch less than a freestyle blade) to allow for tighter footwork. The rocker or curve of the blade is more pronounced than a freestyle blade for quicker edges, and usually the toe pick is a bit smaller, both to avoid scratching the ice and because it isn't needed for big jumps.

Figure Skates

Here I'm referring to the skates worn for the now-dying discipline of figures, as in making tracings of various figures (like the figure-eight) on the ice. Since there's no jumping at all in figures, the boots are much softer, and much more like a dance boot than a freestyle boot. The blades are long like a freestyle blade, but the bottom pick of the toe pick is removed or greatly reduced, so the blade has a continuous surface from heel to toe. (Since figures often require the skater to glide extremely long distances between pushes, having the bottom toe pick scratching the ice would lose too much speed and be a major problem.)
Instead of buying new figure skates, lots of skaters instead take their old, broken-down freestyle skates, slap a pair of figure blades on them (or just grind the bottom toe pick off the old freestyle blades), and just use those.

Rental Figure Skates

Plastic boots and butter-knives for blades, they're everyone's favorite form of self-torture... But they've got toe picks, and boys think their friends are sissies if they wear them instead of the hockey skates, so I guess they must be figure skates.

Often the only thing you can find at your local sporting goods store, they're cheap and usually shoddily constructed, sometimes using canvas or vinyl that's actually flimsier than a rental skate. But there are some decent ones out there too, just make sure your pair has reasonable ankle support.
See "Purchasing" below.

Maintenance

"Booties" or "soakers" (a towel with an elastic band that wraps around your blades) to protect the blades and keep them dry in storage,

"Guards" (plastic blade covers) for walking around in your skates when you're not on the ice. They keep the blades sharp and they allow you to walk on cement and other non-rubberized surfaces which would damage a bare blade.

The skates should be stored some place with ventilation. Wet leather deteriorates more rapidly and gets smelly.

Once in a while you have to sharpen your blades at a skate-sharpener. How often you get your blades sharpened depends on how often you skate, how sharp you like your blades, and how conscientiously you use your guards. Some do it as frequently as every two weeks, most competitive skaters do it every couple months or so, and beginners can get by with once a year or less if they don't skate much. If you feel your blades slipping sideways across the ice, and the blade feels like a butter knife to your finger, it's time to get them sharpened. It can make a huge difference.

An occasional bit of shoe polish to cover up the scuff marks is the last thing I can think of. It's much easier on the men's black skates than on the women's white ones, for obvious reasons.

Whomever mounts the blades will waterproof the boots too. Skate manufacturers sometimes recommend repeated treatments of waterproofing, but I haven't met a skater yet who does that, or a skate-sharpener who recommends it, so I'd say it's just the manufacturers trying to cover themselves in case something does go wrong.

Purchasing

A decent entry-level pair can usually be found for $100 or less. Most all-year rinks have skate shops attached, and you can often get good advice there or from a coach. The skate shops are usually a safe place to buy too. Entry level skates almost always come with the blades already mounted.

At the beginning almost everyone buys a stock boot, that is, a mass-produced boot in a standard size. Most skaters who skate a lot (every day or so) move to the more expensive custom boots, where someone will take measurements of their feet and build the boots specifically to that foot and the level and type of the skater.

Skate Manufacturer Links (in alphabetical order):

Harlick: http://harlick.com

Jackson: http://jacksonskates.com

Klingbeil: http://klingbeilskatingboots.com

Reidell: http://riedellskates.com

SP Teri: http://spteri.com

The constant rubbing of the boots on your ankles can do funny things. My ankles, thick with calluses, were the first part of my body to get hairy as I entered pre-puberty. I thought it was pretty cool.